SOLUTION: A water tower 30 m tall is located at the top of a hill. From a distance of 120 m down the hill it is observed that the angled formed between the top and base of the tower is 8°.

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Question 1205123: A water tower 30 m tall is located at the top of a hill. From a distance of 120 m down the hill it is observed that the angled formed between the top and base of the tower is 8°. Find the angle of inclination of the hill.
Found 2 solutions by amarjeeth123, Edwin McCravy:
Answer by amarjeeth123(569)   (Show Source): You can put this solution on YOUR website!
To find the angle of inclination of the hill, we can use trigonometric ratios. Let's denote the angle of inclination of the hill as θ.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the side opposite the angle θ is the height of the water tower (30 m), and the side adjacent to the angle θ is the distance down the hill (120 m).
tan(θ) = opposite/adjacent
tan(θ) = 30/120
tan(θ) = 1/4
Solve for θ by taking the inverse tangent (arctan) of both sides of the equation.
θ = arctan(1/4)
Using a calculator or a trigonometric table, we can find the value of θ to be approximately 14.04°.
Therefore, the angle of inclination of the hill is approximately 14.04°.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
The solution above is incorrect. 

Let the tower be CT. It's a very steep hill.
The hill is AC. The observer is down at A.



We use the law of sines on triangle ACT

 









This is the ambiguous case ASS, but since we know θ is acute,



Angle θ and angle BAT are complementary, so

Angle BAT = 

So the angle of inclination of the hill is angle BAC

Angle BAC = Angle BAT - 8o = 56.17263736o - 8o = 48.17263736o.

Edwin
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